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When there is a linear relationship between two variables x and y, there is a correlation between them (vol. 44). The numerical value representing the degree of correlation is called a “single correlation coefficient.” It is also called “Pearson’s correlation coefficient.”
[Figure]
As shown in the figure above, when the single correlation coefficient is close to ±1, the relationship between the two variables is linear. The linear relationship weakens as you move away from ±1, and when that value is close to 0, there is no linear relationship between the items.
In other words, as the value of the single correlation coefficient approaches ±1, the correlation becomes stronger, and conversely, as it approaches 0, it becomes weaker. No correlation is observed if the value is 0. Conversely, even if the correlation is only 0.05, there is still a correlation, albeit a weak one.
Therefore, although there are differences in the strengths and weaknesses, in most cases, there is a correlation. Therefore, it is important to determine whether a strong correlation exists. However, there is no statistical standard that says “the correlation is strong if there are more than a few”; standards are determined by each analyst based on their empirical judgment.
The table below presents a general standard (not an absolute standard determined by statistics). If a single correlation coefficient is negative, this table can be applied using the absolute value (takes a negative sign). For example, suppose that the single correlation coefficient between the number of hospital beds per 100,000 people and the inpatient medical expenses per person is +0.71. Since the absolute value of 0.71 falls within the range of “0.5 to 0.8” in this table, it can be said that there is a relationship between the two items.
[Table] Criteria for single correlation coefficients
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